# Optimal integration of DGs into radial distribution network in the presence of plug-in electric vehicles to minimize daily active power losses and to improve the voltage profile of the system using bio-inspired optimization algorithms

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## Abstract

### Purpose

The increase in plug-in electric vehicles (PEVs) is likely to see a noteworthy impact on the distribution system due to high electric power consumption during charging and uncertainty in charging behavior. To address this problem, the present work mainly focuses on optimal integration of distributed generators (DG) into radial distribution systems in the presence of PEV loads with their charging behavior under daily load pattern including load models by considering the daily (24 h) power loss and voltage improvement of the system as objectives for better system performance.

### Design/methodology/approach

To achieve the desired outcomes, an efficient weighted factor multi-objective function is modeled. Particle Swarm Optimization (PSO) and Butterfly Optimization (BO) algorithms are selected and implemented to minimize the objectives of the system. A repetitive backward-forward sweep-based load flow has been introduced to calculate the daily power loss and bus voltages of the radial distribution system. The simulations are carried out using MATLAB software.

### Findings

The simulation outcomes reveal that the proposed approach definitely improved the system performance in all aspects. Among PSO and BO, BO is comparatively successful in achieving the desired objectives.

### Originality/value

The main contribution of this paper is the formulation of the multi-objective function that can address daily active power loss and voltage deviation under 24-h load pattern including grouping of residential, industrial and commercial loads. Introduction of repetitive backward-forward sweep-based load flow and the modeling of PEV load with two different charging scenarios.

## Keywords

Plug-in electric vehicles (PEVs) Distributed generators (DGs) Repetitive distribution power flow Particle swarm optimization algorithm (PSO) Butterfly optimization (BO) Daily active power loss## 1 Introduction

DG (Distributed Generator) is characterized as a local power source with a constrained size associated with the distribution network. DGs Technology has turned into the focal point of consideration for various researchers because it is considered a proper answer for the shortage of electric power supply. Moreover, proper installation of DGs in the distribution system increases the efficiency of the system, improves voltage profile and voltage stability of the system and release of line loading. However, improvement in the above mentioned technical parameters mostly depends on finding the right locations and proper sizing of DGs which is termed as the optimal allocation of DGs. Therefore, an optimal allocation of DGs in a distribution system aims to determine the optimal locations and optimal sizes of DGs to meet active power loss reduction, voltage profile improvement, etc., subject to various constraints such as power demand, voltage limit, DGs size, Maximum power injection by DGs, etc.

Some authors have presented a review of the optimal allocation of DGs in the distribution system [1, 2]. Various researchers have developed a variety of methods for the optimal allocation of DGs in radial distribution networks [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]. Satish Kumar et al. proposed a simulated annealing algorithm for the sizing of multiple DGs to reduce system active power loss. Loss sensitivity indexes have been used for finding locations for DGs [3]. Abu-Mount et al. proposed an artificial honey bee colony technique for the optimal allocation of DGs for the minimization of active power losses in the network [11]. Martín García et al. proposed the optimal allocation of DGs in the distribution network utilizing a modified teaching learning-based optimization algorithm with a goal of minimization of active power losses [8]. It has been observed that finding locations and sizes of DGs simultaneously yields good results rather than finds locations by sensitivity indices and then the size of DGs by an optimization algorithm. Therefore, in this paper, the simultaneous optimal allocation of DGs has been implemented using two bio-inspired optimization algorithms.

Many researchers have developed a weighted factor multi-objective function to gain multiple benefits due to the optimal placement of DGs in the distribution system. El-Zonkoly presented Particle Swarm Optimization for the optimal sitting of various DGs in a distribution network including voltage-dependent load models by aggregated weighted multi-objective optimization approach [13]. Sultana et al. formulated a weighted factor multi-objective function which addresses three benefits of optimal placement of DGs: power loss reduction, voltage profile improvement, and voltage stability improvement [12]. The quasi oppositional teaching learning-based optimization algorithm has used for the minimization of multi-objective function. Mohamed et al. presented a bacterial foraging optimization algorithm for minimization of multi-objective function which comprises power loss, voltage deviation and operating cost of the system [7]. Attia El-Fergany presented a backtracking search algorithm based on the optimal allocation of DGs in the distribution network. Aggregated weight adaptive objective function is utilized to reduce the system’s active power losses and upgrade the voltage profile [9].S K Injeti, presented a Pareto optimization-based improved differential search algorithm for optimal allocation of DGs in radial distribution networks to minimize total operating cost, bus voltage deviation, and active power losses simultaneously [6]. In these papers, the authors considered the optimal allocation of DGs under peak load condition only. It has been observed that the minimization of a multi-objective function gives a trade-off solution between active power loss reduction, voltage deviation minimization, and voltage stability improvement. So, in this paper, we have formulated a weighted factor multi-objective function which will addresses minimization of power loss and voltage deviation for simultaneous optimal allocation of DGs under time varying load pattern (with different load models) of the distribution system.

Some authors have addressed the optimal placement of DGs by considering few load levels of the distribution system. R. S Rao et al. presented a method for optimal placement of DGs in different load levels under an optimally reconfigured network for power loss minimization [4]. B Poornazaryan et al. proposed a new index for optimal allocation of DG units to minimize active power losses and to enhance voltage stability margin by considering load variations. Linear load variations from 50% to 150% of base load with a step size of 1% and in each step size optimal DGs sizes are obtained [10]. Neeraj K et al. proposed an improved cat swarm optimization algorithm for optimal placement of DG and distributed static compensator under a multilevel load profile for power loss minimization [15]. Neeraj Kanwar et al. proposed a new methodology to provide an integrated solution for the optimal allocation of distributed generators and network reconfiguration considering load patterns of customers for the maximization of annual energy loss reduction [5]. In these papers, researchers have concentrated on the optimal placement of DGs under few load levels or linear load variations from 50% to 150% of base load. But a practical distribution system consists of a combination of residential buses, commercial buses, and industrial buses. Linear load variation is not possible for such a distribution system. Because a particular hour in a day if the residential bus load level is 0.8 p.u with respect to peak level 1p.u, the commercial bus load level may be other than 0.8 p.u. Due to uneven load level among the different types of buses, the optimal locations of DGs may vary hour by hour or may not be the same, which increases the complexity of the problem. Therefore, in this paper, we have formulated a weighted multi-objective function addresses daily active power loss minimization; daily voltage profile improvement of a distribution system consists of residential, commercial and industrial loads with 24-h load pattern.

The developing worries over CO_{2} emissions and the greenhouse effect have motivated the shift towards the zero-emission plug-in battery fueled electric vehicles (PEVs) which are expected to play a noteworthy part in making the road transport system. Authors [16, 17] addressed dynamic economic dispatch problem by integrating PEVs charging profiles into a 24-h load demand in an economic and environmental dispatch problem. A detailed review of electric vehicle technologies and the impact of PEVs electric demand on load profiles were given in [18]. Kejun Qian et al. proposed a methodology for modeling of PEVs battery charging load and study the impacts of PEVs on distribution system performance under four charging scenarios [19]. Four charging scenarios are modeled and simulated based on the charging behavior of the vehicles. LI Hui-ling et al. presented the impacts of PEVs charging behavior on distribution grid [20]. However few papers have addressed the mitigation of impacts of PEVs load under different charging behavior via optimal placement of DGs in the distribution system.

In this paper, two PEVs charging scenarios, off-peak charging scenario and peak charging scenarios that are modeled using charging time probability distribution are considered. These two charging time probability functions are measured with a certain number of PEVs and then integrated into the daily load pattern of the distribution system which consists of residential, commercial and industrial buses. Then a detailed analysis of the impacts of the PEVs behavior under two charging scenarios is addressed. As PEVs deteriorate distribution system performance, in this paper DGs are considered to improve the performance of the distribution system with PEVs which requires optimal allocation of DGs. Like the aforementioned, a weighted multi-objective function is formulated for optimal allocation of multiple DGs (power factor-based) in a distribution system with PEVs. Two optimization algorithms PSO and BO are very popular and efficient chosen for optimization of the proposed objective function.

The remaining of the paper is organized as follows; section 2 formulates a mathematical model for optimal allocation of DGs in distribution system with PEVs charging followed by section 3 the implementation of PSO and BO algorithms to the proposed optimization problem has been presented. Section 4 gives the comparative analysis between the distribution system without PEVs and with PEVs charging scenarios and also presented the comparison between without DGs and with DGs on distribution system with PEVs.

## 2 Problem formulation

### 2.1 Modeling of DGs

*P*

_{DG}) and reactive power output (

*Q*

_{DG}). In this type of modelling, active power and power factor (PF) of the DG is mentioned. Reactive power of the DG is calculated by using Eq. 1.

Where *P*_{load}, *Q*_{load} active and reactive power demands at the bus are, *P*_{eff, load}, *Q*_{eff, load} are the effective active and reactive power demands at the bus after the placement of DG.

### 2.2 Objective function

Where, *w1* and *w2* are weighting factors, *PLRI*- Power loss reduction index and *VDIRI*- voltage deviation index reduction index. The range of weighting factors is 0 to 1, which are user-defined. The sum of the weighting factors should always be equal to one.

#### 2.2.1 Power loss reduction index (PLRI)

*PLRI*which is taken as the ratio of system daily active power loss after placement of DGs (\( {P}_{loss, daily}^{DG} \)) to the system daily active power loss before placement of DGs (

*P*

_{loss, daily}).

Where *P*_{jloss} is the *j*^{th} hour system active power loss before placement of DGs [22], \( {P}_{jloss}^{DG} \) is the *j*^{th} hour system active power loss after placementhe t of DGs.

#### 2.2.2 Voltage deviation index reduction index (VDIRI)

*VDIRI*which is the ratio of voltage deviation index with DGs to the voltage deviation index without DGs.

Where, |*U*_{j, i}| the voltage magnitude of *i*^{th} bus is during *j*^{th} hour in p.u before placement of DGs \( \left|{U}_{j,i}^{DG}\right| \) is the voltage magnitude of *i*^{th} bus during *j*^{th} hour in p.u after placement of DGs.

#### 2.2.3 Constraints

- 1.
Active power and reactive power balance constraints.

*P*

_{j, sub}is the

*j*

^{th}hour active power demand supplied by sub-station in kW,

*P*

_{j, D}is

*j*

^{th}hour total active power demand of the system with

*PEV*s in kW,

*Q*

_{j, sub}is the

*j*

^{th}hour reactive power supplied by sub-station in kVAr,

*Q*

_{j, D}is the j

^{th}hour total reactive power demand of the system with

*PE*Vs in kVAr, |

*U*

_{j, sub}| is the substation bus voltage during

*j*

^{th}hour in kV, |

*I*

_{1}| is the 1st branch current in amps during

*j*

^{th}hour,

*P*

_{bus j, i}is the

*i*

^{th}bus active power demand during

*j*

^{th}hour,

*P*

_{PEV j, i}is the

*i*

^{th}bus active power demand due to

*PEV*s in

*j*

^{th}hour.

- 2.
The voltage magnitude of each bus should be within the minimum and maximum voltage limits.

- 3.
The sizes of DGs to be placed should be within minimum and maximum kW limit.

- 4.
Total active power compensation by DGs should be less than or equal to the maximum total capacity of DGs (\( {P}_{T, DG}^{max} \)) which is the user-defined variable and minimum total active power demand throughout the day.

### 2.3 PEVs charging scenario

*PEV*s various researches modeled different types of charging scenarios [19]. They are peak charging scenario (PCS), off-peak charging scenario (OPCS) and stochastic charging scenario (SCS). In the peak charging scenario case, all the PEVs come home after working hours and go for charging as soon as they return from the working place. This charging behavior of

*PEV*s leads to an increase in peak demand of the system because the load on the system is already peaky during those hours. In the case of OPCS, due to electricity prices implemented by the system operator the active power demand due to PEVs shift towards the light demand hours generally at midnight. In SCS,

*PEV*s go for charging at any time in a day. In this paper, PCS and OPCS are considered for the inclusion of

*PEV*s electric demand in the system. The charging time probability distribution of PCS and OPCS are taken from [17] and given in Fig. 1. These two charging time probability functions are measured with a certain number of

*PEV*s to obtain

*P*

_{PEV j, i}and then integrated into daily load pattern of the distribution system which consists of residential, commercial and industrial buses.

## 3 Implemented optimization algorithms

PSO and BO bio-inspired algorithms are chosen for the optimization of the proposed objective function. From the literature, it has been observed that PSO was very old (1995) and well-proven optimization algorithm for solving engineering optimization problems because its advantages like easy to understand and implementation had driven the authors to choose this algorithm. In order to check whether the PSO had given a better solution or not, a comparative analysis has been made based on the latest (2018) optimization algorithm BO. BO algorithm is a newly developed optimization algorithm that has advantages like the new way of information propagation about the agent’s fitness in the form of fragrance, no memory requirement i.e. no need to remember of agent’s individual best positions reached so far.

### 3.1 Particle swarm optimization

Where \( {\overline{\mathrm{V}}}_{\mathrm{i}}^{\mathrm{k}} \) is the velocity vector of *i*^{th} particle at *k*^{th} iteration and each value of the vector should between *V*_{i,min} *≤* \( {V}_i^k \) *≤ V*_{i,max}, \( \overline{\ {\mathrm{x}}_{\mathrm{i}}^{\mathrm{k}}} \) is the current position vector of *i*^{th} particle at *k*^{th} iteration, \( \overline{x_i^{best,k}} \) is the best position vector of *i*^{th} particle up to *k*^{th} iteration, \( \overline{{\mathrm{G}}_{\mathrm{i}}^{\mathrm{best},\mathrm{k}}} \) is the best position vector among all the particles up to *k*^{th} iteration, *W* is the weighing function or inertia weight factor, *W* is the weighing function or inertia weight factor, C_{1} and C_{2} are the acceleration constant, *R*_{1} and *R*_{2} is the random number between 0 and 1.

### 3.2 Butterfly optimization

Where f is the perceived magnitude of the fragrance, i.e., fragrance receiving property by other butterflies, c is the sensory modality, I is the stimulus intensity and *a* is the power exponent dependent on modality, which accounts the varying degree of absorption. Most of the cases a & *c* ∈ [0, 1]. If a = 1, means there is no absorption of fragrance, i.e., the amount of fragrance emitted by a particular butterfly is sensed in the same capacity by the other butterflies (fragrance propagation in an idealized environment). Thus, a butterfly emitting fragrance can be sensed from anywhere in the domain which in turn helps to reach the global optimum easily. On the other hand, if a = 0, it means that the fragrance emitted by any butterfly cannot be sensed by the other butterflies at all. Another important parameter c ∈ [0, ∞] determines the convergence speed. The values of *a* and *c* are crucially affecting the convergence speed of the algorithm. For the maximization problem, the intensity can be proportional to the objective function [25].

- 1.
Every butterfly is supposed to emit some fragrance which enables the butterflies to attract each other (propagation of information).

- 2.
Every butterfly will move randomly or toward the best butterfly emitting more fragrance.

- 3.
The stimulus intensity of a butterfly is affected or determined by the topography of the objective function.

### 3.3 Implementation of PSO and BO algorithms to a proposed problem

Step 1: Initialization of problem and algorithm parameters.

In the first step, the algorithm parameters such as population size (*POP*), dimension of the problem (d), the maximum number of iterations (*itermax*) and for PSO algorithm acceleration constants c1, c2 for BO algorithm probability switch *P*, power exponent *a* and sensor modality *c*are initialized. Initialize the problem parameters such as maximum total capacity of DGs injection \( \left({P}_{T, DG}^{max}\right) \), minimum and maximum bus voltage limits (|*U*_{min}|, |*U*_{max}|), DGs minimum and maximum active power limits (*P*_{DGmin}, *P*_{DGmax}), DGs location limits.

Step 2: Read the Test system Bus and Branch data, p.u demand of different types of buses for a.

day with respect to peak demand, read the probability distribution of PEVs charging scenarios PCS and OPCS. From the p.u demand of the buses and probability distribution of PEVs, kW and kVAr demand of each bus for every hour are obtained.

Step 3: Run the repetitive backward-forward sweep load flow. Calculate the daily active power.

Loss of the system without DGs (*P*_{loss, daily}), voltage deviation index of the system without DGs (*VDI*^{WODG}) of the system.

Step 4: Random generation of locations for DGs placement, DGs sizes within the specified.

*r*epresents locations and DGs sizes, i.e.,

*j*

^{th}population

*i*

^{th}DG location and size respectively, which is generated randomly in between the limits as

*x*

_{max, i}and

*x*

_{min, i}are the

*i*

^{th}DG location limits,

*y*

_{max, i}

*and y*

_{min, i}are the

*i*

^{th}DG size limits and rand() is a random number in between 0 and 1.

In the PSO algorithm, *Soln* represents a group of particles or swarms. Each particle is a solution that contains DGs locations and sizes. In BO, *Soln* represents a group of agents.

For the PSO algorithm along with DGs locations and sizes, generate initial velocities of particles between the minimum and maximum velocity limits.

Step 5: Fitness evaluation (Objective function).

Run the repetitive backward-forward sweep based load flow and calculate the fitness value for each initial solution using Eq. 4, Eq.5 and Eq.6 and record the *gbest* solution in case of BO algorithm, \( \overline{{\mathrm{x}}_{\mathrm{i}}^{\mathrm{best},\mathrm{k}}} \), \( \overline{{\mathrm{G}}_{\mathrm{i}}^{\mathrm{best},\mathrm{k}}} \) for the PSO algorithm.

Step 6: Set iteration count = 0.

Step 7: The evolution procedure of PSO and BO algorithms starts from this step.

Update iteration count by 1.

Step 8: For PSO algorithm, update the velocities of particles using Eq.16 and then update DGs.

locations and DGs size position using Eq.17.

For BO algorithm, calculate the fragrance *f*_{N} for each agent or butterfly using Eq. 18 and then perform a global search and local search as follows.

*rand*<

*probability P*perform global search using Eq. 24

*rand*>

*probability*P perform a local search using Eq. 25

Where \( {soln}_j^d(t) \) and \( {soln}_k^d(t) \) are *j*^{th} and *k*^{th} butterflies from the solution space which belongs to the same swarm and *r* is a random number in [0*,* 1].

Step 9: Fitness evaluation (Objective function).

Run the repetitive backward-forward sweep load flow and calculate the fitness value for each new solution using Eq. 4, Eq. 5 and Eq. 6.

Step 10: Update the *gbest* vector in case of BO algorithm, \( \overline{{\mathrm{x}}_{\mathrm{i}}^{\mathrm{best},\mathrm{k}}} \), \( \overline{{\mathrm{G}}_{\mathrm{i}}^{\mathrm{best},\mathrm{k}}} \) in case of PSO.

algorithm.

Step 11: Stopping criterion.

If the iteration count reaches the maximum number of iterations, computation is terminated and prints the results. Otherwise, repeat Step 7 to Step 11.

## 4 Results and discussion

Grouping of Buses data

Bus Type | Bus Numbers |
---|---|

Residential buses | 2,3,5,6,7,8,9,10,13,14,15,16,17,20,21,23,24 |

Commercial buses | 4,11,12,18,19 |

Industrial buses | 22,26,27,28,29,30,31,32,33 |

### 4.1 Analysis of the system without PEVs load and without DGs

### 4.2 Analysis of the system with PEV load and without DGs

To study the effect of additional electric power demand due to PEVs in the electric distribution system, it has been assumed that 50 PEVs per residential bus with a total of 17*50 = 850 PEVs have been considered, where 45% of these PEVs are low hybrid vehicles equipped with 15 kWh batteries, 25% PEVs are medium hybrid vehicles with 25kwh batteries and 30% PEVs are pure battery vehicles with 40 kWh batteries [17]. It is also assumed that all the electric vehicles return to the home with an SOC of 50%. Therefore, total electric demand due to PEVs per residential bus per day is 50*(15*45% + 25*25% + 40*30%) *0.5 = 625 kW and total electric demand needed per day due to PEVs is 625*17 = 10,625 kW.

#### 4.2.1 Analysis of the system with PEVs peak charging and off-peak charging scenarios

Comparison between without and with PEVs load on test system

Parameters | Without PEV load | With PEV load | |
---|---|---|---|

PCS | OPCS | ||

Daily Active power loss of the system in kWhr | 3053 | 4346 | 3756 |

Voltage deviation index in p.u | 1.6984 | 2.0443 | 1.9743 |

Lowest voltage magnitude in p.u | 0.8945 (18th bus, 17th hour) | 0.8398 (18th bus, 16th hour) | 0.8729 (18th bus, 23rd hour) |

Active power demand from the buses for a day in kWhr | 64,510 | 75,135 | 75,135 |

From Table 2 it has been observed that due to PEVs electric active power demand 10,625 kW, the distribution system is overload by 16.47% with respect to daily active power demand requirement. In case of PCS due to extra PEVs active power demand, daily active power loss of the system is increased to 4346 kW from 3053 kW which shows 42.35% increase in daily active power loss whereas in case of OPCS daily active power loss of the system is increased to 3756 kW from 3053 kW which shows 23.02% increase in daily active power loss. Also in the case of PCS, the voltage deviation index is increased to 2.0443p.u and in the case of OPCS, it has increased to 1.9743 p.u. In fact, in both the scenarios (PCS & OPCS) there is an increase in a daily active power loss of the system and voltage profile deterioration. But in the comparison between two charging scenarios, an increase in daily active power loss is 19.33% more in PCS when compared with OPCS and also the difference between voltage deviation indexes of OPCS and PCS is 0.07p.u. From the above observations, it has been concluded that the shifting of PEVs active power demand to light electric demand hours by implementing different electricity pricing on consumers i.e. in case of OPCS shows a greater impact on improvement in reduction in peak active power demand, daily active power loss, and improvement of the voltage profile.

### 4.3 Optimal placement of DGs in the distribution system with consideration of PEVs

Parameters description of PSO and BO algorithms

Parameters for PSO | |
---|---|

Population (pop) | 150 |

Dimension (dim) | 6 (3 DG sizes+ 3 locations) |

Maximum number of iterations ( | 150 |

| 1 |

| 2 |

Parameters for BO | |

Population (pop) | 150 |

Dimension (dim) | 6 (3 DG sizes+ 3 locations) |

Maximum number of iterations ( | 150 |

Modular modality ‘c’ | 0.01 |

Power exponent ‘a’ | 0.1 to 0.3 |

Probability switch ‘P’ | 0.5 |

#### 4.3.1 Optimal placement of DGs (upf)

Result analysis for optimal allocation of DGs at upf

Parameters | BO | PSO |
---|---|---|

DG (upf) size (kW)/Bus number | 309 (10) | 200 (12) |

493 (16) | 500 (16) | |

699 (31) | 776 (31) | |

Daily active Power Loss in kw | 1563 | 1590 |

% Daily active power loss reduction | 58.39 | 57.66 |

Voltage deviation Index In p.u | 0.8063 | 0.8091 |

Lowest voltage of the system in p.u | 0.9353 (18th bus, 23rd hour) | 0.933 (18th bus, 23rd hour) |

OF | 0.4139 | 0.4193 |

PLRI | 0.4161 | 0.4233 |

VDIRI | 0.4087 | 0.4098 |

Time in sec | 305.9 | 376.56 |

#### 4.3.2 Optimal placement of DGs at 0.9pf

Result analysis for optimal allocation of DGs at 0.9 pf

Parameters | BO | PSO |
---|---|---|

DG (0.9 pf) size (kW)/Bus number | 628 (15) | 452 (17) |

459 (30) | 200 (10) | |

413 (32) | 828 (31) | |

Daily active Power Loss in kw | 870 | 916 |

% Daily active power loss reduction | 76.84 | 75.61 |

Voltage deviation Index In p.u | 0.5238 | 0.5404 |

Lowest voltage of the system in p.u | 0.9498 (18th bus, 23rd hour) | 0.9496 (14th bus, 23rd hour) |

OF | 0.2417 | 0.2528 |

PLRI | 0.2316 | 0.2439 |

VDIRI | 0.2653 | 0.2737 |

Time in sec | 309.8 | 410 |

## 5 Conclusions

In this paper, a 33-bus radial distribution test system consists of a residential, commercial, and an industrial bus is considered. A 24-h load pattern of the whole test system is obtained from the load pattern of different types of buses. Two charging scenarios PCS and OPCS had taken for the inclusion of PEVs load demand on the system. The impact of PEVs load demand on the system has been analyzed through technical parameters. Among the two charging scenarios PCS and OPCS, the impact of PEVs load with the OPCS charging scenario had less impact on the system technical parameters. A combined 24-h load pattern of the system including PEVs load demand with OPCS charging scenario has been considered for the optimal placement of the DGs in the system. A weighted objective function has designed to reduce the Daily active power loss and Voltage deviation index using repetitive backward/forward sweep load flow. Two algorithms BO and PSO have been selected and implemented for the minimization of the proposed objective function. From the obtained results it can be concluded that the radial distribution system performance (reduction in daily active power loss and system voltage profile) in the presence of PEVs loads including daily load pattern has improved with the optimal integration of DGs by the proposed approach. Among PSO and BO based approaches, BO performs better in terms of solution quality and convergence. Most of the practical/engineering optimization problems are multi-objective in nature which is found to be difficult by solving using traditional approaches. In this context, optimization algorithms will pave a way to solve the most of the non-linear engineering optimization problems.

## Notes

### Acknowledgments

Authors were indebting thankful to the Department of Science and Technology (DST-SERB), Govt. of India, New Delhi for funding this research project EEQ-2016-000263. The authors were also thankful to the Director NIT Warangal and the department of Electrical Engineering for their valuable support towards the smooth execution of the project.

### Author’s contributions

Both authors equally contributed to the work presented in the paper and approved the final manuscript.

### Funding

Proposal Number: EEQ-2016-000263, Financially supported by Department of Science and Technology (**DST**), Science and Engineering Research Board (**SERB**), Govt. of India, New Delhi, India.

### Ethical approval and consent to participate

Not Applicable.

### Consent for publication

Not Applicable.

### Competing interests

The authors declare that they have no competing interests.

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